A pipe can fill a tank in 10 hours, while another pipe can empty it in 15 hours.
Practice Questions
Q1
A pipe can fill a tank in 10 hours, while another pipe can empty it in 15 hours. If both pipes are opened together, how long will it take to fill the tank?
5 hours
6 hours
7 hours
8 hours
Questions & Step-by-Step Solutions
A pipe can fill a tank in 10 hours, while another pipe can empty it in 15 hours. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: 30 hours
Step 1: Determine the rate at which the first pipe fills the tank. It fills the tank in 10 hours, so its rate is 1 tank per 10 hours, or 1/10 of the tank per hour.
Step 2: Determine the rate at which the second pipe empties the tank. It empties the tank in 15 hours, so its rate is 1 tank per 15 hours, or 1/15 of the tank per hour.
Step 3: Calculate the net rate of filling the tank when both pipes are opened together. This is done by subtracting the emptying rate from the filling rate: (1/10) - (1/15).
Step 4: To subtract the fractions, find a common denominator. The least common multiple of 10 and 15 is 30.
Step 5: Convert the rates to have the common denominator: (1/10) = 3/30 and (1/15) = 2/30.
Step 6: Now subtract the two rates: (3/30) - (2/30) = 1/30.
Step 7: The net rate of filling the tank is 1/30 of the tank per hour. This means it takes 30 hours to fill the tank when both pipes are open.
Rate of Work – Understanding how to calculate the rates of filling and emptying a tank and combining them.
Fractional Work – Using fractions to represent the portion of the tank filled or emptied per hour.
Net Rate Calculation – Calculating the net effect of two opposing rates (filling and emptying) to find the overall rate.
